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klio [65]
3 years ago
14

Which equation could be used to solve the problem? Sarah spent $160 on lunch in 10 weeks. If she spent the same amount every wee

k, how much did she spend on lunch each week (w)? A. w = 160 ÷ 10 B. w = 160 – 10 C. w = 10 • 160 D. w = 10 ÷ 160
Mathematics
1 answer:
ser-zykov [4K]3 years ago
6 0
The correct answer would be A, because 160/10 is getting you your unit rate, or the amount Sarah spent every week.
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Sove the equation and verify
Nostrana [21]

Let's break the equation in several step to make things more clear: first of all, the numerator of the left hand side simplifies to

\dfrac{2x}{3}-\dfrac{1}{2} = \dfrac{4x-3}{6}

Similarly, the denominator becomes

\dfrac{3x}{4}-\dfrac{1}{2} = \dfrac{3x-2}{4}

Dividing by a fraction means to multiply by the inverse of that fraction:

\dfrac{\frac{a}{b}}{\frac{c}{d}} = \dfrac{a}{b}\cdot\dfrac{d}{c}

So, in your case, we have

\dfrac{\frac{2x}{3}-\frac{1}{2}}{\frac{3x}{4}-\frac{1}{2}} = \dfrac{\frac{4x-3}{6}}{\frac{3x-2}{4}} = \dfrac{4x-3}{6}\cdot \dfrac{4}{3x-2} = \dfrac{2(4x-3)}{3(3x-2)} = \dfrac{8x-6}{9x-6}

So, the equation has become

\dfrac{8x-6}{9x-6} = \dfrac{4}{3}

Multiply both sides by 3(9x-6):

3(8x-6) = 4(9x-6) \iff 24x-18 = 36x-24

Subtract 24x from both sides, and add 18 to both sides:

36x-24x = 24-18 \iff 12x=6 \iff x = \dfrac{1}{2}

8 0
4 years ago
Y= 1/3x-9
notka56 [123]

Answer:

y=3x+28

Step-by-step explanation:

so a line perpendicular to one with a slope of 1/3 would have a slope of 3/1 which is just 3

so your line would be y=3x+b

to find b you just plug in the coordinates of the point that you want it to pass through into x and y. Remember that points are written as (x,y)

10=3x-6+b

10=-18+b

28= b

the equation is y=3x+28

6 0
3 years ago
Inverse laplace transform of H(s) = 1/(s+4)^2
ziro4ka [17]

Answer:

Inverse Laplace of \frac{1}{(S+4)^2} will be te^{-4t}

Step-by-step explanation:

We have to find the inverse Laplace transform of H(S)=\frac{1}{(S+4)^2}

We know that of \frac{1}{s+4} is e^{-4t}

As in H(s) there is square of s+4

So i inverse Laplace there will be multiplication of t

So the inverse Laplace of \frac{1}{(s+4)^2}  will be te^{-4t}

L^{-1}\frac{1}{(S+4)^2}=te^{-4t}

4 0
4 years ago
What is the value of the expression =2 ?<br> 0<br> 2
Valentin [98]
2 is the answer because 2=2 but 2 doesn’t =0.
6 0
4 years ago
Read 2 more answers
What is the distance between the points (5, -1) and (5,<br> 3)
Diano4ka-milaya [45]

By using distance formula (which is attached below), you can solve this problem:

√(x2-x1)^2+(y2-y1)^2

(5, -1) and (5, 3)

√(5-5)^2+(3-(-1))^2

√0^2+4^2

√0+16

√16

4

The distance between the two points is 4.

7 0
3 years ago
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